Home
Class 12
MATHS
If two points are taken on the minor axi...

If two points are taken on the minor axis of an ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is `2a^2dot`

A

`a^(2)`

B

`b^(2)`

C

`2a^(2)`

D

`2b^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION-C ( Objective Type Questions ( More than one answer))|1 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION-C|45 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise Assignment (SECTION - A)|55 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise section-J (Aakash Challengers Qestions)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise section - J|6 Videos

Similar Questions

Explore conceptually related problems

If two points are taken on the mirror axis of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 at the same distance from the centre as the foci, then the sum of the sequares of the perpendicular distance from these points on any tangent to the ellipse is

Product of perpendiculars drawn from the foci upon any tangent to the ellipse 3x^(2)+4y^(2)=12 is

The locus of the foot of the perpendicular drawn from the centre on any tangent to the ellipse x^2/25+y^2/16=1 is:

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

The locus of the foot of the perpendicular from the foci an any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

Prove that the product of the perpendiculars from the foci upon any tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is b^(2)

Find the eccentric angle of a point on the ellipse (x^(2))/(6)+(y^(2))/(2)=1 whose distance from the center of the ellipse is sqrt(5)

Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.

AAKASH INSTITUTE-CONIC SECTIONS-SECTION-B
  1. The equation of the chord of the ellipse x^(2) + 4y^(2) = 4 having th...

    Text Solution

    |

  2. The radius of the circle passing through the foci of (x^(2))/(16) + (y...

    Text Solution

    |

  3. If two points are taken on the minor axis of an ellipse (x^2)/(a^2)...

    Text Solution

    |

  4. Find the locus of the foot of the perpendicular drawn from the cent...

    Text Solution

    |

  5. find the common tangents of the circle x^2+y^2=2a^2 and the parabola...

    Text Solution

    |

  6. The line lx + my + n = 0 is a normal to (x^(2))/(a^(2)) + (y^(2))/(b^...

    Text Solution

    |

  7. The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(...

    Text Solution

    |

  8. From a point P, two tangents are drawn to the parabola y^(2) = 4ax. I...

    Text Solution

    |

  9. The centre of the ellipse 4x^(2) + 9y^(2) + 16 - 18y - 11 = 0 is

    Text Solution

    |

  10. The length of the latus rectum of the ellipse 2x^(2) + 3y^(2) - 4x -...

    Text Solution

    |

  11. The co-ordinates of foci of an ellipse 3x^(2) + 4y^(2) - 4x - 6y -13 =...

    Text Solution

    |

  12. If the line joining foci subtends an angle of 90^(@) at an extremity ...

    Text Solution

    |

  13. In an ellipse the distance between the foci is 8 and the distance betw...

    Text Solution

    |

  14. Tangents are drawn to the ellipse x^2/9+y^2/5 = 1 at the end of latus ...

    Text Solution

    |

  15. The tangent at any point on the ellipse 16x^(2) + 25^(2) = 400 meets ...

    Text Solution

    |

  16. If tangents are drawn to the ellipse 2x^(2) + 3y^(2) =6, then the locu...

    Text Solution

    |

  17. The minimum area of the triangle formed by the tangent to the ellipse ...

    Text Solution

    |

  18. The number of common tangents to the ellipse (x^(2))/(16) + (y^(2))/(9...

    Text Solution

    |

  19. If the focal distance of an end of minor axis of any ellipse, ( whose...

    Text Solution

    |

  20. Number of points on the ellipse (x^(2))/(25) + (y^(2))/(16) =1 from wh...

    Text Solution

    |